Properties

Label 4840.197
Modulus $4840$
Conductor $4840$
Order $44$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4840, base_ring=CyclotomicField(44))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,22,11,34]))
 
pari: [g,chi] = znchar(Mod(197,4840))
 

Basic properties

Modulus: \(4840\)
Conductor: \(4840\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4840.cq

\(\chi_{4840}(197,\cdot)\) \(\chi_{4840}(373,\cdot)\) \(\chi_{4840}(637,\cdot)\) \(\chi_{4840}(813,\cdot)\) \(\chi_{4840}(1077,\cdot)\) \(\chi_{4840}(1253,\cdot)\) \(\chi_{4840}(1517,\cdot)\) \(\chi_{4840}(1957,\cdot)\) \(\chi_{4840}(2133,\cdot)\) \(\chi_{4840}(2397,\cdot)\) \(\chi_{4840}(2573,\cdot)\) \(\chi_{4840}(2837,\cdot)\) \(\chi_{4840}(3013,\cdot)\) \(\chi_{4840}(3277,\cdot)\) \(\chi_{4840}(3453,\cdot)\) \(\chi_{4840}(3717,\cdot)\) \(\chi_{4840}(3893,\cdot)\) \(\chi_{4840}(4157,\cdot)\) \(\chi_{4840}(4333,\cdot)\) \(\chi_{4840}(4773,\cdot)\)

sage: chi.galois_orbit()
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: \(\Q(\zeta_{44})\)
Fixed field: 44.44.212907048724487789150739362720525788138562346514417698933058002742934795048229975182497632223232000000000000000000000000000000000.1

Values on generators

\((3631,2421,1937,4721)\) → \((1,-1,i,e\left(\frac{17}{22}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(7\)\(9\)\(13\)\(17\)\(19\)\(21\)\(23\)\(27\)\(29\)
\( \chi_{ 4840 }(197, a) \) \(1\)\(1\)\(i\)\(e\left(\frac{29}{44}\right)\)\(-1\)\(e\left(\frac{13}{44}\right)\)\(e\left(\frac{5}{44}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{37}{44}\right)\)\(-i\)\(e\left(\frac{3}{22}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4840 }(197,a) \;\) at \(\;a = \) e.g. 2